Zero - Because it is represented by a circle, zero may symbolize completeness; or your true self.
(2)It may symbolize 'nothingness' in a sense of worthlessness or emptiness. Perhaps you are being shown the vanity of vanity, the ultimate meaninglessness of worldly ambition and successs, or the ultimate insubstantilaity of the egotistic self.

Seeing a zebra in your dream, represents perfect balance, unity, harmony, and the attraction of opposites. Alternatively, it means that you are spending too much time in trivial and varying matters You need to establish a mindset and lay your groundwork for some solid stability.
Zodiacal Sign - If your own zodiacal sign appears in the dream it may symbolize your shadow.

Zoo - Were you inside the cages? If so, did you feel secure or did you feel constricted? This may be hinting at a situation in waking life.